A note on the symmetric powers of the standard representation of S n

David Savitt, Richard P. Stanley

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Abstract

In this paper, we prove that the dimension of the space spanned by the characters of the symmetric powers of the standard n-dimensional representation of Sn is asymptotic to n2/2. This is proved by using generating functions to obtain formulas for upper and lower bounds, both asymptotic to n2/2, for this dimension. In particular, for n ≥ 7, these characters do not span the full space of class functions on Sn.

Original languageEnglish (US)
Pages (from-to)1-8
Number of pages8
JournalElectronic Journal of Combinatorics
Volume7
Issue number1 R
StatePublished - Dec 1 2000

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics

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